GATE Signals and Systems: LTI Systems and Convolution – Previous Year Questions
9 GATE previous year questions on LTI Systems and Convolution (Signals and Systems, Biomedical Engineering) with answers and explanations, from every paper.
- GATE 2021 BM Q40 – The shown x[n] and h[n] are convolved to give y[n]. If y[2]=1 and y[3]=0, find h[0]. The graph amplitudes are not drawn to scale.
- GATE 2022 BM Q40 – The ideal system has h i(t)=e- tu(t). The real system has delayed response h r(t)=e-(t-T)u(t-T) plus auxiliary path h a(t)=[u(t)-u(t-5T)]. For impulse…
- GATE 2023 BM Q47 – Sequences x₁[n] and x₂[n] have samples [1,2,1] and [1,1,2] respectively for n=0,1,2 and are zero elsewhere. Let x=x₁*x₂. Which statements are correct?
- GATE 2023 BM Q49 – Let x(t)=1 for 0≤t≤1 and zero otherwise, and y(t)=x*x. Which statements are correct?
- GATE 2024 BM Q24 – An LTI system obeys y(t)+y′(t)+0.5y″(t)=x(t)+0.1x′(t). Find the Laplace transform of its impulse response under zero initial conditions.
- GATE 2024 BM Q59 – x[n]=u[n]−u[n−5],h[n]=δ[n]−δ[n−1],and y=x*h. Find the sum of y[n] over all integers n, as an integer.
- GATE 2025 BM Q44 – Systems U,V are defined by U: y(t)=x(t)²+1 and V: y(t)=x(t+1). Which are correct?
- GATE 2025 BM Q47 – An LTI system has h[n]=δ[n]+δ[n−1]/2+δ[n−2]/3. Input is x[n]=δ[n]+δ[n−1]. Which output statements hold?
- GATE 2026 BM Q63 – An LTI system has h[n]=[0,0.6,0.8,0.5,0.3,0] and input x[n]=[1,0.6,0,0,0,0], both indexed from n=0. Find the maximum output sample, rounded to one…